# Sum of Infinite Geometric Sequence/Corollary 2/Mistake

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geometric series

## Mistake

The sum of the finite initial segments of the series is:
$\dfrac {a \paren {r^n - 1} } {r - 1}$,
whence, if the infinite series converges, its sum is $a / \paren {r - 1}$.

## Correction

This should read:

whence, if the infinite series converges, its sum is $a / \paren {1 - r}$.

This is demonstrated in Sum of Infinite Geometric Sequence: Corollary 2.